The Cholesky decomposition technique is commonly used to reduce the memory requirement for storing two-particle repulsion integrals in quantum chemistry calculations that use atomic orbital bases. However, when quantum methods use multicomponent bases, such as nuclear–electronic orbitals, additional challenges are introduced due to asymmetric two-particle integrals. This work proposes several multicomponent Cholesky decomposition methods for calculations using nuclear–electronic orbital density functional theory. To analyze the errors in different Cholesky decomposition components, benchmark calculations using water clusters are carried out. The largest benchmark calculation is a water cluster (H 2 O) 27 where all 54 protons are treated quantum mechanically. This study provides energetic and complexity analyses to demonstrate the accuracy and performance of the proposed multicomponent Cholesky decomposition method.
The Cholesky decomposition technique is commonly used to reduce the memory requirement for storing two-particle repulsion integrals in quantum chemistry calculations that use atomic orbital bases. However, when quantum methods use multicomponent bases, such as nuclear–electronic orbitals, additional challenges are introduced due to asymmetric two-particle integrals. This work proposes several multicomponent Cholesky decomposition methods for calculations using nuclear–electronic orbital density functional theory. To analyze the errors in different Cholesky decomposition components, benchmark calculations using water clusters are carried out. The largest benchmark calculation is a water cluster (H 2 O) 27 where all 54 protons are treated quantum mechanically. This study provides energetic and complexity analyses to demonstrate the accuracy and performance of the proposed multicomponent Cholesky decomposition method.
Cholesky decomposition (CD) is widely used to reduce the cost of storing two-particle integrals and has been extended to multicomponent nuclear–electronic orbital (NEO) methods. Although NEO-CD lowers memory demands, single-node implementations can still face memory bottlenecks due to the size of the mixed asymmetric nuclear–electronic tensors. In this study, we present a two-stage hybrid-layout distributed NEO-CD framework suitable for large NEO calculations at scale. Cholesky vectors are first generated and orthonormalized using an atomic orbital (AO)-index distribution. During Fock matrix construction, mixed nuclear–electronic vectors retain the AO-index layout, while pure electronic and pure nuclear vectors are redistributed over the auxiliary index. This design avoids costly inter-rank communication and provides efficient construction of both Coulomb and exchange matrices. Benchmark calculations on water clusters with all protons treated quantum mechanically show excellent scaling and load balance. Using only 104 MPI ranks, a full NEO-Fock build for (H2O)250 with 500 quantum protons, the largest NEO calculation to date, completes in 96.2 s per Fock matrix construction. The distributed NEO-CD framework enables NEO-DFT calculations for liquid-like water clusters up to (H2O)100. Extrapolation of the binding energies yields a bulk-limit value of ΔEn→∞ = −10.35 ± 0.19 kcal/mol, in excellent agreement with the experimental vaporization enthalpy of water. These results demonstrate that fully quantum mechanical simulations of large molecular systems are now practical on modern computing architectures.
We present in this contribution the first application of local correlation in the context of multicomponent methods. Multicomponent approaches allow for the targeted simulation of electrons together with other Fermions (most commonly protons) as quantum particles. These methods have become increasingly popular over the last years, particularly for the description of nuclear quantum effects (in strong hydrogen bonds, proton tunneling, and many more). However, most implementations are still based on canonical formulations of wave function theory, which we know for decades to be computationally inefficient for capturing dynamical correlation effects. Local correlation approaches, particularly with the use of pair natural orbitals (PNOs), enable asymptotically linear scaling of computational costs with very little impact on the overall accuracy. In this context, the efficient use of density fitting approximations in the integral calculation proves essential. We start by discussing our implementation of density-fitted NEO-MP2 and NEO-PNO-LMP2, upgrading the electronic correlation treatment up to PNO local coupled cluster level of theory. Several challenging examples are provided to benchmark the method in terms of accuracy as well as computational cost scaling. Following appropriate protocols, anharmonic corrections to localized X-H stretches can be applied routinely with little computational overhead.
The variational quantum eigensolver (VQE) algorithm combined with the unitary coupled cluster (UCC) ansatz has been developed for the quantum computation of molecular energies and wave functions within the Born–Oppenheimer approximation. Herein, this approach is extended to multicomponent systems to enable the quantum mechanical treatment of more than one type of particle, such as electrons and positrons or electrons and nuclei, without invoking the Born–Oppenheimer approximation. Specifically, we introduce the multicomponent unitary coupled cluster (mcUCC) method combined with the VQE algorithm for the calculation of ground-state energies and wave functions as well as the multicomponent equation-of-motion (mcEOM) method for the calculation of excitation energies. These methods are developed within the nuclear-electronic orbital (NEO) framework and are formulated in the qubit basis to enable implementations on quantum computers. Moreover, these methods are used to calculate the ground-state energy and excitation energies of positronium hydride, where both electrons and the positron are treated quantum mechanically, as well as the H 2 molecule, where both electrons and one proton are treated quantum mechanically. These applications validate the implementation and provide benchmark data for future calculations. The errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism, as well as the accompanying computer code, will serve as the basis for applications to more complex multicomponent systems, such as simulations of photoinduced nonadiabatic molecular processes, on both classical and quantum computers.
This work targets the development and application of low-order scaling multicomponent methods for efficient simulation of nuclear quantum effects (NQE) within complex systems. The awareness of NQEs is increasingly growing across various fields, including chemistry, biology, and materials science, where light nuclei, like protons, play an essential role in molecular interactions and properties. This thesis presents a systematic development and application of multicomponent methods based on the Nuclear-Electronic Orbital (NEO) framework developed by Hammes-Schiffer and coworkers. In general, the focus is placed on the implementation and optimization of multicomponent Hartree-Fock, density functional and Møller-Plesset perturbation theory, as well as composite correlation approaches. Overall, by addressing computational bottlenecks and notably expanding the scope of multicomponent methods, this work contributes to the development of an extended standard quantum chemistry toolbox and paves the way for routine simulations of NQEs.
Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems is presented. This method provides a balanced treatment of many-particle correlation in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is the extension of the electronic structure CCSD formulation for multicomponent systems and is defined as ∣ΨmcCC⟩=eT1I+T2I+T1II+T2II+T11I,II+T12I,II+T21I,II+T22I,II∣0I0II⟩. The applicability of the mcCC method was demonstrated by computing biexciton binding energies for multiexcitonic systems and benchmarking the results against full configuration interaction calculations. The results demonstrated that connected cluster operators that generate simultaneous excitation in type I and type II space are critical for capturing electron-hole correlation in multiexcitonic systems.
In the present work, we show the feasibility of using single precision in quantum chemistry, especially regarding the computation of electron correlation energy. On the example of the MP2 method, we clearly demonstrate that single precision arithmetic is sufficient for evaluating the molecular two-electron integrals by the use of the Cholesky decomposition method. The evaluation of integrals with single precision arithmetic introduces a negligible error into the computed MP2 correlation energy. In particular, the corresponding error in the MP2 correlation energy amounts to only 10(-7)Eh for the 113-atom taxol molecule in double-valence basis set (1099 basis functions). The practical relevance of our result is that 50% performance gain and 50% reduction in memory demands can be achieved by only minor changes in the existing codes. Our finding opens intriguing perspectives for doing accurate correlated quantum chemistry on specialized floating-point mathematical coprocessors.